Manufacturers use process analysis and structural analysis in designing a wide variety of products, including consumer goods, automotive parts, electronic equipment, and medical equipment. It is often advantageous to simulate or otherwise model a manufacturing process to aid in the development of a particular product. A computer simulation of a manufacturing process may allow accurate prediction of how changes in process variables and/or product configuration will affect production. By performing process simulation, a designer can significantly reduce the time and cost involved in developing a product, since computer modeling reduces the need for experimental trial and error. Computer-aided process simulation allows for optimization of process parameters and product configuration during the early design phase, when changes can be implemented more quickly and less expensively.
A manufacturer may also use modeling to predict structural qualities of a manufactured product, such as how the product will react to internal and external forces after it is made. A structural model may be used, for instance, to predict how residual stress in a molded product may result in product warpage. Structural models aid in the design of a product, since many prospective versions of the design can be tested before actual implementation. Time-consuming trial and error associated with producing and testing actual prototypes can be greatly reduced.
There is increasing demand for uniquely designed components. This is particularly true in the field of plastics manufacturing, where uniquely adaptable materials may be formed into a myriad of configurations using processes such as injection molding, compression molding, thermoforming, extrusion, pultrusion, and the like. This is also true in the manufacturing of parts made with fiber-filled materials, composites, and other specialty materials, custom-designed for specialized uses.
Process and structural analysis in these fields poses significant challenges. For example, there is increasing demand for products having complex geometries. In order to properly model a molding process for a product having a complex geometry, the mold must be adequately characterized by the solution domain of the model. Modeling processes involving components with complex geometries requires significantly more computational time and computer resources than modeling processes involving components with simple geometries.
Also, injection-molded plastic is viscoelastic and may have highly temperature-dependent and shear-dependent properties. These complexities further increase computational difficulty of process and structural simulations involving plastic components. Governing equations of adequate generality must be solved over complex domains, taking into account the changing properties of the material being processed. Analytical solutions of these equations over complex domains are generally unavailable; thus, numerical solutions must be sought.
Computer models use numerical methods to approximate the exact solution of governing equations over complex geometries, where analytical solutions are unavailable. A model of an injection molding process may include, for example, a solution domain in the shape of the mold interior, discretized to enable accurate numerical approximation of the solution of the applicable governing equations over the solution domain.
Process models often simulate molds having complicated shapes by using solution domains with simplified geometries, thereby reducing required computation time and computer resources. For example, certain injection molding process simulators use a two-dimensional (2D) solution domain to simplify the geometry of the real, three-dimensional (3D) mold, thereby greatly reducing computational complexity. Many of these simulators use a Hele-Shaw solution approach, where pressure variation and fluid flow in the thickness direction are assumed to be zero. These “2.5D” models are generally beneficial for simulating injection molding of thin-walled components having relatively simple geometries. However, in components that have thick portions or complex geometries, injected material flows in all three directions, and traditional thin-wall assumptions do not apply, making the 2.5D analysis inadequate.
Current 3D models of injection molding processes do not make thin-wall assumptions; they solve constitutive equations over a three-dimensional solution domain. These models are computationally complex, generally requiring significantly greater computer resources and computation times for process simulation than the simpler 2.5D models. Three-dimensional models of injection molding processes generally use a finite element scheme in which the geometry of the mold is simulated with a mesh of 3D elements. The size of the elements, or the discretization, required to accurately model a given process depends on the geometry of the solution domain and the process conditions. The generation of a 3D mesh is not trivial, and there is currently no consistent method of automatically generating a suitable 3D mesh for a given application.
Determining a suitable mesh for a 2.5D, Hele-Shaw-based model is also non-trivial. For example, it is typically necessary to define a surface representing the midplane of a thin-walled component, which is then meshed with triangular or quadrilateral elements to which appropriate thicknesses are ascribed. Thus, there is an added step of determining a midplane surface that must be performed after defining solution domain geometry.
Many manufactured components have at least some portion that is thin-walled or shell-like, that may be amenable to simulation using a 2.5D model. However, many of these components also have one or more thick or complex portions in which the 2.5D assumptions do not hold, thereby making the overall analysis inaccurate. One may use a 3D model to more comprehensively simulate processing of components that have both thick and thin portions. However, the computational complexity of a 3D model is much greater than that of a 2.5D model, thereby increasing the time and computer resources required for analysis.
Additionally, the way a 3D model must be discretized further reduces the efficiency of a 3D process model for a component having thin portions. For example, a typical thin portion of a molded component may have a thickness of about 2 mm, whereas the length of the thin portion may be hundreds of millimeters. During the molding process, there will generally be a large thermal gradient across the thickness of the thin portion, perhaps hundreds of degrees per millimeter, whereas the temperature gradient along the length of the portion (transverse to the thickness) may be extremely low. Conversely, the pressure gradient in the thickness direction will generally be very low, while the pressure gradient in the transverse direction will be very high. The high variability of these properties in at least two directions—temperature across the thickness, and pressure along the length—calls for a very dense mesh with many solution nodes in order to achieve an accurate process simulation, thereby increasing computational complexity. Thus, the time required for accurate 3D simulation of a typical component containing both a thick and a thin portion may be as much as a day or more and may require significant computer resources, due to the fine discretization required.
Hybrid simulations solve simplified flow equations in the relatively thin regions of a given component and more complex flow equations in other regions. Hybrid simulations may reduce the computational complexity associated with full 3D models while improving the simulation accuracy associated with 2.5D models.
A hybrid solution scheme has been proposed in Yu et al., “A Hybrid 3D/2D Finite Element Technique for Polymer Processing Operations,” Polymer Engineering and Science, Vol. 39, No. 1, 1999. The suggested technique does not account for temperature variation and, thus, does not provide accurate results in non-isothermal systems where material properties vary with temperature, as in most injection molding systems. Example applications of the technique involve relatively simple solution domains that have been pre-divided into “2D” and “3D” portions. Furthermore, there does not appear to be a suggestion of how to adapt the technique for the analysis of more complex parts than the examples shown.
U.S. Pat. No. 6,161,057, issued to Nakano, suggests a simple hybrid solution scheme that solves for process variables in a thick portion and a thin portion of a solution domain. The suggested technique requires simplifying assumptions to calculate pressure and fluid velocity in both the thick and thin portions of the solution domain. For example, the technique requires using Equation 1, below, to calculate fluid velocity in the thick portion of the solution domain:
                                          υ            x                    =                      ξ            ⁢                                          ∂                P                                            ∂                x                                                    ,                              υ            y                    =                      ξ            ⁢                                          ∂                P                                            ∂                y                                                    ,                              υ            z                    =                      ξ            ⁢                                          ∂                P                                            ∂                z                                                                        (        1        )            where υx, υy, and υz are fluid velocity in the x, y, and z directions, respectively; P is pressure; and ξ is flow conductance, which is defined in the Nakano patent as a function of fluid viscosity. The approximation of Equation 1 is more akin to the 2.5D Hele Shaw approximation than full 3D analysis, and Equation 1 does not adequately describe fluid flow in components having thick and/or complex portions, particularly where the thick portion makes up a substantial (nontrivial) part of the component.
Current modeling methods are not robust; they must be adapted for use in different applications depending on the computational complexity involved. Modelers decide which modeling method to use based on the process to be modeled and the geometry of the component to be produced and/or analyzed. Modelers must also determine how to decompose a solution domain into elements depending on the particular component and process being simulated. The decisions made in the process of choosing and developing a model for a given component and/or process may well affect the accuracy of the model output. The process of adapting models to various applications is time-consuming and generally involves significant customization by a highly-skilled technician.
There is a need for a more accurate, more robust, faster, and less costly method of modeling manufacturing processes and performing structural analyses of manufactured components. Current methods require considerable input by a skilled technician and must be customized for the component and/or process being modeled.